A Theory AB Toolbox

Marco Gaboardi, Justin Hsu

Randomized algorithms are a staple of the theoretical computer science
literature. By careful use of randomness, algorithms can achieve properties
that are simply not possible with deterministic algorithms. Today, these
properties are proved on paper, by theoretical computer scientists; we
investigate formally verifying these proofs.
The main challenges are two: proofs about algorithms can be quite complex,
using various facts from probability theory; and proofs are highly
customized---two proofs of the same property for two algorithms can be
completely different. To overcome these challenges, we propose taking
inspiration from paper proofs, by building common tools---abstractions,
reasoning principles, perhaps even notations---into a formal verification
toolbox. To give an idea of our approach, we consider three common patterns in
paper proofs: the union bound, concentration bounds, and martingale arguments.